Find the perimter and area of a 45-45-90 degree triangle with hypotenuse length of 10 centimeters.
P=20 square root 2 cm?
A=50 cm ^2
This is just a right triangle... Use SOHCAHTOA to solve for each side and you can find the perimeter... Area of a triangle =b*h/2
Each leg is 10/√2, so
P = 2*10/√2 + 10 = 10(1+√2)
A = (1/2)(10/√2)(10/√2) = 100/4 = 25
To find the perimeter and area of a 45-45-90 degree triangle, you need to know the length of one side. In this case, the hypotenuse length is given as 10 centimeters.
In a 45-45-90 degree triangle, the two legs are congruent and the hypotenuse is times the length of a leg. So, the length of each leg can be found by dividing the hypotenuse length by square root of 2.
Length of each leg = (hypotenuse length) / √2
Length of each leg = 10 cm / √2
Length of each leg ≈ 7.07 cm (rounded to two decimal places)
Now that we have the length of one side, we can find the perimeter and area of the triangle.
Perimeter of a triangle = sum of all three sides
Perimeter of the 45-45-90 triangle = 7.07 cm + 7.07 cm + 10 cm
Perimeter of the triangle ≈ 24.14 cm (rounded to two decimal places)
Area of a triangle = (base * height) / 2
Since this is an isosceles triangle, any leg can be called the base, and the corresponding height is the length perpendicular to the base, which is also a leg.
Area of the 45-45-90 triangle = (7.07 cm * 7.07 cm) / 2
Area of the triangle ≈ 24.99 cm^2 (rounded to two decimal places)
Therefore, the perimeter of the triangle is approximately 24.14 cm and the area is approximately 24.99 cm^2.